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					                                   SAFT Model
                                   Associating Hard Sphere Chains
                                   Molecules with a Single Associating Site - Dimerizing Fluid
                                   Walter G. Chapman

                                   Equation of State Parameters
Site Volume                        K_AA =        1.87E-03             Z = 1 + m (Z_HS - 1) + Z_chain + Z_assoc
Site Energy                        E_AA/kT =             7 < 700
Chain Length                       m=                    2
                                                                      Hard Sphere Results

                                  Packing         Molecular Hard     Hard      Hard
                                  Fraction        Density   Sphere   Sphere    Sphere    rho * d g_HS
                                  Pi/6 rho d^3    rho d^3   P d^3/kT Z         g_HS(d) / drho
                                     1.00E-05      9.55E-06 0.00002 1.00004 1.000025 2.5E-05
                                         0.025     0.023873 0.05283 1.106543 1.065426 0.068469
                                          0.05     0.047746 0.11721 1.227438 1.137192 0.150398
                             18
                                         0.075      0.07162 0.19550 1.364835 1.216118 0.248431
                             16             0.1    0.095493 0.29054 1.521262 1.303155 0.365798
    Compressibility Factor




                                         0.125     0.119366 0.40578 1.699708 1.399417 0.506456
                             14           0.15     0.143239 0.54538 1.903725 1.506208 0.675279
                                                                                     Hard Sphere
                             12          0.175     0.167113 0.71442 2.137546 1.625066 0.878305
                                            0.2    0.190986 0.91912 2.40625 1.757813 1.123047
                             10          0.225                                       Non-associating
                                                   0.214859 1.16710 2.715954 1.906616 1.418917
                              8           0.25                                       Fluid
                                                   0.238732 1.46776 3.074074 2.074074 1.777778
                                         0.275     0.262606 1.83280 3.489647 2.263315 2.214678
                              6                                                      Associating Fluid
                                            0.3    0.286479 2.27680 3.973761 2.478134 2.748855
                              4          0.325     0.310352 2.81807 4.540111 2.723162 3.405082
                                          0.35     0.334225 3.47978 5.205735 3.004096 4.215539
                              2          0.375     0.358099 4.29145      5.992     3.328    5.2224
                                            0.4    0.381972 5.29102 6.925926 3.703704 6.481481
                              0
                                         0.425     0.405845 6.52761 8.041999 4.142352 8.067438
                               0.00 0.10  0.45     0.20 0.30 0.40 0.50 4.658152 10.08128
                                                   0.429718 8.06553 9.384673
                                             Packing Fraction
                    X_0 = 1 / ( 1 + rho X_0 Delta )
Z_chain + Z_assoc
                    d X_0 / d rho = - X_0^2 [Delta + rho d Delta / d rho] / [ 1 + 2 X_0 rho Delta]

                                        Associating Contribution

                              Fract. of                                             Chain Contribution
rho * d g_HS                  Monomers d X_0 /                                      to the Eqn. of State
                    Delta     X_0          d rho     Z_assoc                        Z_chain
                     2.044503 0.9999805 -2.04439 -9.76164E-06                         -2.5E-05
                     2.178212 0.9527928 -1.91475 -0.025120489                         -0.06426
                     2.324934 0.9083981 -1.80767       -0.05185829                    -0.13225
                          9
                     2.486293 0.8663493 -1.71744 -0.080476553                         -0.20428
                          8
                     2.664237 0.8262944 -1.64008 -0.111232545                          -0.2807
                      2.86104 0.7879613 -1.57278 -0.144388249                          -0.3619
                          7
                      Pressure d^3/kT




d Sphere             3.079369 0.7511362 -1.51346 -0.180218554                         -0.44833 Hard Sphere
                          6
                     3.322369 0.715648 -1.46055 -0.219018294                          -0.54047
                     3.593762 0.6813586 -1.41286       -0.26110893                    -0.63889
 associating              5 0.6481549 -1.36945 -0.306845399
                     3.897984                                                         -0.74421 Non
                     4.240344 0.6159439 -1.32958 -0.356623562
                          4                                                           -0.85714 Fluid
                     4.627239 0.5846486 -1.29265 -0.410888649                         -0.97851
ociating Fluid            3                                                                    Associating Fluid
                     5.066425 0.554205 -1.25815        -0.47014512                    -1.10924
                     5.567373 0.5245601 -1.22568 -0.534968413
                          2                                                           -1.25041
                      6.14173 0.4956698 -1.19489 -0.606019182                         -1.40326
                          1
                     6.803935 0.4674976 -1.16547 -0.684060764                         -1.56923
                     7.572042 0.4400139 -1.13717 -0.769980868                             -1.75
                          0
                     8.468838 0.4131948 -1.10975 -0.864818786                         -1.94755
                           0.00       0.10      0.20    0.30
                     9.523365 0.3870217 -1.08302 -0.969799909    0.40             0.50-2.16422
                                                      Packing Fraction
0 rho Delta]



Chain Contribution                              Compressibility Factor for an Associating
to the Eqn. of State          Non-associating
                    Non-associating             Hard Sphere Chain Fluid
                              Pd^3/kT
                    Z_hard_chain                Z = 1 + m (Z_HS - 1) + Z_chain + Z_assoc
                     1.000055 0.00001            1.000045
                      1.14882 0.02743               1.1237
                     1.322623 0.06315            1.270765
                     1.525388 0.10925            1.444912
                     1.761822 0.16824             1.65059
                     2.037512 0.24321            1.893124
          Hard Sphere2.359119 0.33792               2.1789
                     2.734619 0.45699            2.515601
                     3.173611 0.60612            2.912502
          Non-associating
                     3.687702 0.79234            3.380856
          Fluid      4.291005 1.02440            3.934382
                     5.000783 1.31323            4.589895
          Associating Fluid
                     5.838278 1.67254            5.368133
                     6.829807 2.11965            6.294839
                     8.008207 2.67655            7.402188
                     9.414769 3.37142            8.730708
                     11.10185 4.24060            10.33187
                     13.13645 5.33136            12.27163
                     15.60512 6.70581            14.63532
Pressure for an Associating
Hard Sphere Chain Fluid
P d^3 / kT
  0.00001
  0.02683
  0.06067
  0.10348
  0.15762
  0.22598
  0.31210
  0.42039
  0.55625
  0.72641
  0.93926
  1.20533
  1.53786
  1.95362
  2.47400
  3.12645
  3.94648
  4.98038
  6.28907

				
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posted:7/3/2011
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